Friday, April 27, 2012

All the usual websites will get that functionality eventually, but I got a little impatient and decided to write a little Sealed Simulator for Avacyn Restored before the prerelease.

The programming is pretty straightforward - it's a bit of jQuery plus a ton of code which every single language other than Javascript has in its Standard library already. If you want to see what some quick and dirty code I write looks like, help yourself.

Writing this simulator made me realize how little we know about what actually gets into boosters.
We know there will be:

1 card from rare sheet (7/8 rare, 1/8 mythic)

3 uncommons

either 10 commons, or 9 commons and 1 foil

1 basic land

Do we know what percentage of time there's a foil card in the booster? And what are rarity ratios of foil cards? That's what I've been told - I have no way to verify it, but it sounds plausible enough. And that's about it.

Things we don't know about boosters

One much more important thing is which commons and uncommons we're going to get.

If cards were chosen independently random, 55% of boosters in small set and 37% of boosters in large sets would contain duplicate common cards by birthday paradox. This happens almost 0% of the time.

Software simulators always use explicit deduplication to deal with this particular issue, and that's where they all stop (as far as I know, my simulator definitely does), but that's not how actual paper cards are printed.

Real world cards are printed into sheets in some specified order (the same card can appear on the sheet more than once, in different context, so it's not that regular - for example on the rare sheet each rare occurs twice and each mythic occurs once), cut into individual cards, and then mixed into boosters by some predefined method.

People attempt to figure out these "print runs" mostly so they can figure out how rares are printed - then they can buy a few boxes, open a few boosters which will have money rares and mythics in them (plus a few more boosters needed to figure that out) - and then sell the rest on ebay to unsuspecting players who will than receive various junk rares.

For Limited simulators rares don't matter all that much. Actually it does in that Limited played by taking completely random boosters, and Limited played by taking consecutive boosters from a box will have different statistics - but simulators can faithfully have the same distribution of rares as you'd get in Limited if you used truly random boosters, so it's close enough.

What matters the most for Limited is print runs of commons and uncommons. By taking commons entirely at random, the way all simulators do (except for deduplicating step) you get highly non-uniform distribution of colors - you'll very likely get ton of commons in some colors and very few in some other colors. This means that in simulated Sealed pools it's usually really easy to make very high quality deck with two colors which just happen to be most numerous, and some other colors are pretty much impossible to include other than as splash for a bomb.

Real paper Sealed tends to have more equal rates, so you're not so railroaded into colors. Maybe you can make about equally good RG werewolves and UW fliers deck from the same pool? This ambiguity is pretty common in paper and much less common on simulators.

How important it is? Honestly, I have no idea. I'd love to be able to do some math, and it's possible to model the method used by the simulators (we have the source code), but I don't have enough information to model paper boosters. I find it strange that WotC never wrote any articles about it (I duckduckwent them - there were really none), except mentioning a few major related screw ups they've done in remote past. Have they been secretive, or is there just not enough interest?

Another interesting question - and one which should be much easier to answer - does MTGO use print runs? We have tons of MTGO drafts recorded, if someone could simply get them together, and run simple statistics like % of commons by color in each booster we should be able to at least determine if they select them by uniform random methods or some other way, even if we don't know the particulars of that other way.

EDIT: I thought this only matters for Sealed not Draft (since you're getting 1-2 card from 8 different boosters anyway in each round, not 14 cards from 1 booster, so it should even out), but I've been told by people who draft Cube (which generally doesn't use print runs) that uniform randomness makes any kind of color signaling pretty much impossible. So it matters a hue deal, just for a different reason.

My software

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Unless otherwise expressly stated, all original material of whatever nature created by Tomasz Węgrzanowski and included in this blog, is licensed under a Creative Commons License. It is also licensed under GFDL (for Wikipedia compatibility).